Minimization of the potential energy surface of Lennard–Jones clusters by quantum optimization

One of the most widely used strategies for global optimization employs the concept of classical simulated annealing. In the last decade an alternative approach has been suggested based on quantum simulated annealing. Here, we apply quantum annealing ideas to finding minimum energy structures of Lennard–Jones clusters. We find that quantum annealing is superior to classical simulated annealing but is affected by ergodicity breaking difficulties similar to classical simulated annealing. This difficulty is particularly serious for larger clusters with multiple funnel potential energy surfaces. ! 2005 Elsevier B.V. All rights reserved. Finding the atomic structure that corresponds to the global minimum of the potential energy surface (PES) is a central problem in cluster physics. It is highly nontrivial as for most global optimization problems: (i) the PES has many local minima, whose number grows exponentially with cluster size and (ii) the PES usually has a multi-funnel structure, reflecting the simultaneous presence of competing growth sequences. Both features are present in Lennard–Jones (LJ) clusters, in spite of the relative simplicity of the inter-atomic interactions given by the two-body potential